Properties

Label 2640.2.d.i.529.1
Level $2640$
Weight $2$
Character 2640.529
Analytic conductor $21.081$
Analytic rank $0$
Dimension $6$
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2640,2,Mod(529,2640)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2640, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2640.529");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2640 = 2^{4} \cdot 3 \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2640.d (of order \(2\), degree \(1\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(21.0805061336\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.0.350464.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 165)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 529.1
Root \(0.403032 - 0.403032i\) of defining polynomial
Character \(\chi\) \(=\) 2640.529
Dual form 2640.2.d.i.529.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000i q^{3} +(-1.48119 - 1.67513i) q^{5} -2.80606i q^{7} -1.00000 q^{9} +O(q^{10})\) \(q-1.00000i q^{3} +(-1.48119 - 1.67513i) q^{5} -2.80606i q^{7} -1.00000 q^{9} +1.00000 q^{11} +5.11871i q^{13} +(-1.67513 + 1.48119i) q^{15} +4.54420i q^{17} -4.57452 q^{19} -2.80606 q^{21} +4.00000i q^{23} +(-0.612127 + 4.96239i) q^{25} +1.00000i q^{27} +2.38787 q^{29} +0.962389 q^{31} -1.00000i q^{33} +(-4.70052 + 4.15633i) q^{35} +1.61213i q^{37} +5.11871 q^{39} -2.38787 q^{41} +2.80606i q^{43} +(1.48119 + 1.67513i) q^{45} +4.31265i q^{47} -0.873992 q^{49} +4.54420 q^{51} +6.57452i q^{53} +(-1.48119 - 1.67513i) q^{55} +4.57452i q^{57} -13.2750 q^{59} +7.92478 q^{61} +2.80606i q^{63} +(8.57452 - 7.58181i) q^{65} -10.7005i q^{67} +4.00000 q^{69} +7.35026 q^{71} -6.41819i q^{73} +(4.96239 + 0.612127i) q^{75} -2.80606i q^{77} +1.35026 q^{79} +1.00000 q^{81} -0.806063i q^{83} +(7.61213 - 6.73084i) q^{85} -2.38787i q^{87} +2.96239 q^{89} +14.3634 q^{91} -0.962389i q^{93} +(6.77575 + 7.66291i) q^{95} -9.92478i q^{97} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 2 q^{5} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 2 q^{5} - 6 q^{9} + 6 q^{11} - 4 q^{19} - 16 q^{21} - 2 q^{25} + 16 q^{29} - 16 q^{31} + 12 q^{35} - 12 q^{39} - 16 q^{41} - 2 q^{45} - 22 q^{49} + 8 q^{51} + 2 q^{55} - 16 q^{59} + 4 q^{61} + 28 q^{65} + 24 q^{69} + 24 q^{71} + 8 q^{75} - 12 q^{79} + 6 q^{81} + 44 q^{85} - 4 q^{89} - 16 q^{91} + 44 q^{95} - 6 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2640\mathbb{Z}\right)^\times\).

\(n\) \(661\) \(881\) \(991\) \(1057\) \(1201\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(-1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.00000i 0.577350i
\(4\) 0 0
\(5\) −1.48119 1.67513i −0.662410 0.749141i
\(6\) 0 0
\(7\) 2.80606i 1.06059i −0.847812 0.530296i \(-0.822081\pi\)
0.847812 0.530296i \(-0.177919\pi\)
\(8\) 0 0
\(9\) −1.00000 −0.333333
\(10\) 0 0
\(11\) 1.00000 0.301511
\(12\) 0 0
\(13\) 5.11871i 1.41968i 0.704365 + 0.709838i \(0.251232\pi\)
−0.704365 + 0.709838i \(0.748768\pi\)
\(14\) 0 0
\(15\) −1.67513 + 1.48119i −0.432517 + 0.382443i
\(16\) 0 0
\(17\) 4.54420i 1.10213i 0.834462 + 0.551065i \(0.185778\pi\)
−0.834462 + 0.551065i \(0.814222\pi\)
\(18\) 0 0
\(19\) −4.57452 −1.04947 −0.524733 0.851267i \(-0.675835\pi\)
−0.524733 + 0.851267i \(0.675835\pi\)
\(20\) 0 0
\(21\) −2.80606 −0.612333
\(22\) 0 0
\(23\) 4.00000i 0.834058i 0.908893 + 0.417029i \(0.136929\pi\)
−0.908893 + 0.417029i \(0.863071\pi\)
\(24\) 0 0
\(25\) −0.612127 + 4.96239i −0.122425 + 0.992478i
\(26\) 0 0
\(27\) 1.00000i 0.192450i
\(28\) 0 0
\(29\) 2.38787 0.443417 0.221708 0.975113i \(-0.428837\pi\)
0.221708 + 0.975113i \(0.428837\pi\)
\(30\) 0 0
\(31\) 0.962389 0.172850 0.0864250 0.996258i \(-0.472456\pi\)
0.0864250 + 0.996258i \(0.472456\pi\)
\(32\) 0 0
\(33\) 1.00000i 0.174078i
\(34\) 0 0
\(35\) −4.70052 + 4.15633i −0.794533 + 0.702547i
\(36\) 0 0
\(37\) 1.61213i 0.265032i 0.991181 + 0.132516i \(0.0423056\pi\)
−0.991181 + 0.132516i \(0.957694\pi\)
\(38\) 0 0
\(39\) 5.11871 0.819650
\(40\) 0 0
\(41\) −2.38787 −0.372923 −0.186462 0.982462i \(-0.559702\pi\)
−0.186462 + 0.982462i \(0.559702\pi\)
\(42\) 0 0
\(43\) 2.80606i 0.427921i 0.976842 + 0.213960i \(0.0686363\pi\)
−0.976842 + 0.213960i \(0.931364\pi\)
\(44\) 0 0
\(45\) 1.48119 + 1.67513i 0.220803 + 0.249714i
\(46\) 0 0
\(47\) 4.31265i 0.629065i 0.949247 + 0.314532i \(0.101848\pi\)
−0.949247 + 0.314532i \(0.898152\pi\)
\(48\) 0 0
\(49\) −0.873992 −0.124856
\(50\) 0 0
\(51\) 4.54420 0.636315
\(52\) 0 0
\(53\) 6.57452i 0.903079i 0.892251 + 0.451540i \(0.149125\pi\)
−0.892251 + 0.451540i \(0.850875\pi\)
\(54\) 0 0
\(55\) −1.48119 1.67513i −0.199724 0.225875i
\(56\) 0 0
\(57\) 4.57452i 0.605909i
\(58\) 0 0
\(59\) −13.2750 −1.72826 −0.864131 0.503266i \(-0.832132\pi\)
−0.864131 + 0.503266i \(0.832132\pi\)
\(60\) 0 0
\(61\) 7.92478 1.01466 0.507332 0.861751i \(-0.330632\pi\)
0.507332 + 0.861751i \(0.330632\pi\)
\(62\) 0 0
\(63\) 2.80606i 0.353531i
\(64\) 0 0
\(65\) 8.57452 7.58181i 1.06354 0.940408i
\(66\) 0 0
\(67\) 10.7005i 1.30728i −0.756807 0.653639i \(-0.773242\pi\)
0.756807 0.653639i \(-0.226758\pi\)
\(68\) 0 0
\(69\) 4.00000 0.481543
\(70\) 0 0
\(71\) 7.35026 0.872316 0.436158 0.899870i \(-0.356339\pi\)
0.436158 + 0.899870i \(0.356339\pi\)
\(72\) 0 0
\(73\) 6.41819i 0.751192i −0.926783 0.375596i \(-0.877438\pi\)
0.926783 0.375596i \(-0.122562\pi\)
\(74\) 0 0
\(75\) 4.96239 + 0.612127i 0.573007 + 0.0706823i
\(76\) 0 0
\(77\) 2.80606i 0.319781i
\(78\) 0 0
\(79\) 1.35026 0.151916 0.0759582 0.997111i \(-0.475798\pi\)
0.0759582 + 0.997111i \(0.475798\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 0.806063i 0.0884770i −0.999021 0.0442385i \(-0.985914\pi\)
0.999021 0.0442385i \(-0.0140861\pi\)
\(84\) 0 0
\(85\) 7.61213 6.73084i 0.825651 0.730062i
\(86\) 0 0
\(87\) 2.38787i 0.256007i
\(88\) 0 0
\(89\) 2.96239 0.314013 0.157006 0.987598i \(-0.449816\pi\)
0.157006 + 0.987598i \(0.449816\pi\)
\(90\) 0 0
\(91\) 14.3634 1.50570
\(92\) 0 0
\(93\) 0.962389i 0.0997950i
\(94\) 0 0
\(95\) 6.77575 + 7.66291i 0.695177 + 0.786198i
\(96\) 0 0
\(97\) 9.92478i 1.00771i −0.863789 0.503854i \(-0.831915\pi\)
0.863789 0.503854i \(-0.168085\pi\)
\(98\) 0 0
\(99\) −1.00000 −0.100504
\(100\) 0 0
\(101\) −13.6121 −1.35446 −0.677229 0.735773i \(-0.736819\pi\)
−0.677229 + 0.735773i \(0.736819\pi\)
\(102\) 0 0
\(103\) 16.3127i 1.60733i 0.595080 + 0.803667i \(0.297120\pi\)
−0.595080 + 0.803667i \(0.702880\pi\)
\(104\) 0 0
\(105\) 4.15633 + 4.70052i 0.405616 + 0.458724i
\(106\) 0 0
\(107\) 9.43136i 0.911764i 0.890040 + 0.455882i \(0.150676\pi\)
−0.890040 + 0.455882i \(0.849324\pi\)
\(108\) 0 0
\(109\) 15.4010 1.47515 0.737576 0.675264i \(-0.235970\pi\)
0.737576 + 0.675264i \(0.235970\pi\)
\(110\) 0 0
\(111\) 1.61213 0.153016
\(112\) 0 0
\(113\) 13.7381i 1.29238i 0.763179 + 0.646188i \(0.223638\pi\)
−0.763179 + 0.646188i \(0.776362\pi\)
\(114\) 0 0
\(115\) 6.70052 5.92478i 0.624827 0.552488i
\(116\) 0 0
\(117\) 5.11871i 0.473225i
\(118\) 0 0
\(119\) 12.7513 1.16891
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) 2.38787i 0.215307i
\(124\) 0 0
\(125\) 9.21933 6.32487i 0.824602 0.565713i
\(126\) 0 0
\(127\) 12.4182i 1.10194i −0.834526 0.550968i \(-0.814259\pi\)
0.834526 0.550968i \(-0.185741\pi\)
\(128\) 0 0
\(129\) 2.80606 0.247060
\(130\) 0 0
\(131\) −5.92478 −0.517650 −0.258825 0.965924i \(-0.583335\pi\)
−0.258825 + 0.965924i \(0.583335\pi\)
\(132\) 0 0
\(133\) 12.8364i 1.11306i
\(134\) 0 0
\(135\) 1.67513 1.48119i 0.144172 0.127481i
\(136\) 0 0
\(137\) 9.79877i 0.837165i 0.908179 + 0.418583i \(0.137473\pi\)
−0.908179 + 0.418583i \(0.862527\pi\)
\(138\) 0 0
\(139\) −2.12601 −0.180326 −0.0901628 0.995927i \(-0.528739\pi\)
−0.0901628 + 0.995927i \(0.528739\pi\)
\(140\) 0 0
\(141\) 4.31265 0.363191
\(142\) 0 0
\(143\) 5.11871i 0.428048i
\(144\) 0 0
\(145\) −3.53690 4.00000i −0.293724 0.332182i
\(146\) 0 0
\(147\) 0.873992i 0.0720856i
\(148\) 0 0
\(149\) −8.31265 −0.680999 −0.340499 0.940245i \(-0.610596\pi\)
−0.340499 + 0.940245i \(0.610596\pi\)
\(150\) 0 0
\(151\) 15.2750 1.24307 0.621533 0.783388i \(-0.286510\pi\)
0.621533 + 0.783388i \(0.286510\pi\)
\(152\) 0 0
\(153\) 4.54420i 0.367377i
\(154\) 0 0
\(155\) −1.42548 1.61213i −0.114498 0.129489i
\(156\) 0 0
\(157\) 7.01317i 0.559712i 0.960042 + 0.279856i \(0.0902868\pi\)
−0.960042 + 0.279856i \(0.909713\pi\)
\(158\) 0 0
\(159\) 6.57452 0.521393
\(160\) 0 0
\(161\) 11.2243 0.884595
\(162\) 0 0
\(163\) 6.76116i 0.529575i 0.964307 + 0.264787i \(0.0853018\pi\)
−0.964307 + 0.264787i \(0.914698\pi\)
\(164\) 0 0
\(165\) −1.67513 + 1.48119i −0.130409 + 0.115311i
\(166\) 0 0
\(167\) 11.8192i 0.914600i 0.889312 + 0.457300i \(0.151183\pi\)
−0.889312 + 0.457300i \(0.848817\pi\)
\(168\) 0 0
\(169\) −13.2012 −1.01548
\(170\) 0 0
\(171\) 4.57452 0.349822
\(172\) 0 0
\(173\) 6.99271i 0.531646i −0.964022 0.265823i \(-0.914356\pi\)
0.964022 0.265823i \(-0.0856436\pi\)
\(174\) 0 0
\(175\) 13.9248 + 1.71767i 1.05261 + 0.129843i
\(176\) 0 0
\(177\) 13.2750i 0.997813i
\(178\) 0 0
\(179\) −2.70052 −0.201847 −0.100923 0.994894i \(-0.532180\pi\)
−0.100923 + 0.994894i \(0.532180\pi\)
\(180\) 0 0
\(181\) −21.1998 −1.57577 −0.787885 0.615822i \(-0.788824\pi\)
−0.787885 + 0.615822i \(0.788824\pi\)
\(182\) 0 0
\(183\) 7.92478i 0.585816i
\(184\) 0 0
\(185\) 2.70052 2.38787i 0.198546 0.175560i
\(186\) 0 0
\(187\) 4.54420i 0.332305i
\(188\) 0 0
\(189\) 2.80606 0.204111
\(190\) 0 0
\(191\) −13.1490 −0.951430 −0.475715 0.879599i \(-0.657811\pi\)
−0.475715 + 0.879599i \(0.657811\pi\)
\(192\) 0 0
\(193\) 5.89446i 0.424293i −0.977238 0.212146i \(-0.931955\pi\)
0.977238 0.212146i \(-0.0680453\pi\)
\(194\) 0 0
\(195\) −7.58181 8.57452i −0.542945 0.614034i
\(196\) 0 0
\(197\) 20.3938i 1.45299i 0.687169 + 0.726497i \(0.258853\pi\)
−0.687169 + 0.726497i \(0.741147\pi\)
\(198\) 0 0
\(199\) 17.4010 1.23353 0.616764 0.787148i \(-0.288443\pi\)
0.616764 + 0.787148i \(0.288443\pi\)
\(200\) 0 0
\(201\) −10.7005 −0.754757
\(202\) 0 0
\(203\) 6.70052i 0.470285i
\(204\) 0 0
\(205\) 3.53690 + 4.00000i 0.247028 + 0.279372i
\(206\) 0 0
\(207\) 4.00000i 0.278019i
\(208\) 0 0
\(209\) −4.57452 −0.316426
\(210\) 0 0
\(211\) −18.1260 −1.24785 −0.623923 0.781486i \(-0.714462\pi\)
−0.623923 + 0.781486i \(0.714462\pi\)
\(212\) 0 0
\(213\) 7.35026i 0.503632i
\(214\) 0 0
\(215\) 4.70052 4.15633i 0.320573 0.283459i
\(216\) 0 0
\(217\) 2.70052i 0.183323i
\(218\) 0 0
\(219\) −6.41819 −0.433701
\(220\) 0 0
\(221\) −23.2605 −1.56467
\(222\) 0 0
\(223\) 23.6385i 1.58295i 0.611202 + 0.791475i \(0.290686\pi\)
−0.611202 + 0.791475i \(0.709314\pi\)
\(224\) 0 0
\(225\) 0.612127 4.96239i 0.0408085 0.330826i
\(226\) 0 0
\(227\) 1.26916i 0.0842371i 0.999113 + 0.0421185i \(0.0134107\pi\)
−0.999113 + 0.0421185i \(0.986589\pi\)
\(228\) 0 0
\(229\) −16.1768 −1.06899 −0.534496 0.845171i \(-0.679499\pi\)
−0.534496 + 0.845171i \(0.679499\pi\)
\(230\) 0 0
\(231\) −2.80606 −0.184625
\(232\) 0 0
\(233\) 18.4690i 1.20994i 0.796247 + 0.604971i \(0.206815\pi\)
−0.796247 + 0.604971i \(0.793185\pi\)
\(234\) 0 0
\(235\) 7.22425 6.38787i 0.471258 0.416699i
\(236\) 0 0
\(237\) 1.35026i 0.0877089i
\(238\) 0 0
\(239\) 19.3258 1.25008 0.625042 0.780591i \(-0.285082\pi\)
0.625042 + 0.780591i \(0.285082\pi\)
\(240\) 0 0
\(241\) 28.5501 1.83907 0.919536 0.393006i \(-0.128565\pi\)
0.919536 + 0.393006i \(0.128565\pi\)
\(242\) 0 0
\(243\) 1.00000i 0.0641500i
\(244\) 0 0
\(245\) 1.29455 + 1.46405i 0.0827059 + 0.0935348i
\(246\) 0 0
\(247\) 23.4156i 1.48990i
\(248\) 0 0
\(249\) −0.806063 −0.0510822
\(250\) 0 0
\(251\) −23.1998 −1.46436 −0.732180 0.681112i \(-0.761497\pi\)
−0.732180 + 0.681112i \(0.761497\pi\)
\(252\) 0 0
\(253\) 4.00000i 0.251478i
\(254\) 0 0
\(255\) −6.73084 7.61213i −0.421502 0.476690i
\(256\) 0 0
\(257\) 10.8872i 0.679123i −0.940584 0.339561i \(-0.889721\pi\)
0.940584 0.339561i \(-0.110279\pi\)
\(258\) 0 0
\(259\) 4.52373 0.281091
\(260\) 0 0
\(261\) −2.38787 −0.147806
\(262\) 0 0
\(263\) 9.11871i 0.562284i 0.959666 + 0.281142i \(0.0907132\pi\)
−0.959666 + 0.281142i \(0.909287\pi\)
\(264\) 0 0
\(265\) 11.0132 9.73813i 0.676534 0.598209i
\(266\) 0 0
\(267\) 2.96239i 0.181295i
\(268\) 0 0
\(269\) 11.2995 0.688941 0.344471 0.938797i \(-0.388058\pi\)
0.344471 + 0.938797i \(0.388058\pi\)
\(270\) 0 0
\(271\) −25.1998 −1.53078 −0.765390 0.643567i \(-0.777454\pi\)
−0.765390 + 0.643567i \(0.777454\pi\)
\(272\) 0 0
\(273\) 14.3634i 0.869315i
\(274\) 0 0
\(275\) −0.612127 + 4.96239i −0.0369126 + 0.299243i
\(276\) 0 0
\(277\) 2.41819i 0.145295i −0.997358 0.0726475i \(-0.976855\pi\)
0.997358 0.0726475i \(-0.0231448\pi\)
\(278\) 0 0
\(279\) −0.962389 −0.0576167
\(280\) 0 0
\(281\) 30.4894 1.81885 0.909424 0.415870i \(-0.136523\pi\)
0.909424 + 0.415870i \(0.136523\pi\)
\(282\) 0 0
\(283\) 8.35756i 0.496805i 0.968657 + 0.248403i \(0.0799056\pi\)
−0.968657 + 0.248403i \(0.920094\pi\)
\(284\) 0 0
\(285\) 7.66291 6.77575i 0.453912 0.401361i
\(286\) 0 0
\(287\) 6.70052i 0.395519i
\(288\) 0 0
\(289\) −3.64974 −0.214690
\(290\) 0 0
\(291\) −9.92478 −0.581801
\(292\) 0 0
\(293\) 23.0943i 1.34918i 0.738192 + 0.674591i \(0.235680\pi\)
−0.738192 + 0.674591i \(0.764320\pi\)
\(294\) 0 0
\(295\) 19.6629 + 22.2374i 1.14482 + 1.29471i
\(296\) 0 0
\(297\) 1.00000i 0.0580259i
\(298\) 0 0
\(299\) −20.4749 −1.18409
\(300\) 0 0
\(301\) 7.87399 0.453849
\(302\) 0 0
\(303\) 13.6121i 0.781996i
\(304\) 0 0
\(305\) −11.7381 13.2750i −0.672124 0.760127i
\(306\) 0 0
\(307\) 2.65562i 0.151564i −0.997124 0.0757821i \(-0.975855\pi\)
0.997124 0.0757821i \(-0.0241453\pi\)
\(308\) 0 0
\(309\) 16.3127 0.927994
\(310\) 0 0
\(311\) 15.9756 0.905891 0.452946 0.891538i \(-0.350373\pi\)
0.452946 + 0.891538i \(0.350373\pi\)
\(312\) 0 0
\(313\) 0.0606343i 0.00342726i 0.999999 + 0.00171363i \(0.000545465\pi\)
−0.999999 + 0.00171363i \(0.999455\pi\)
\(314\) 0 0
\(315\) 4.70052 4.15633i 0.264844 0.234182i
\(316\) 0 0
\(317\) 3.81336i 0.214180i 0.994249 + 0.107090i \(0.0341532\pi\)
−0.994249 + 0.107090i \(0.965847\pi\)
\(318\) 0 0
\(319\) 2.38787 0.133695
\(320\) 0 0
\(321\) 9.43136 0.526407
\(322\) 0 0
\(323\) 20.7875i 1.15665i
\(324\) 0 0
\(325\) −25.4010 3.13330i −1.40900 0.173804i
\(326\) 0 0
\(327\) 15.4010i 0.851680i
\(328\) 0 0
\(329\) 12.1016 0.667181
\(330\) 0 0
\(331\) −24.2882 −1.33500 −0.667500 0.744609i \(-0.732636\pi\)
−0.667500 + 0.744609i \(0.732636\pi\)
\(332\) 0 0
\(333\) 1.61213i 0.0883440i
\(334\) 0 0
\(335\) −17.9248 + 15.8496i −0.979335 + 0.865954i
\(336\) 0 0
\(337\) 22.5804i 1.23003i −0.788514 0.615016i \(-0.789149\pi\)
0.788514 0.615016i \(-0.210851\pi\)
\(338\) 0 0
\(339\) 13.7381 0.746153
\(340\) 0 0
\(341\) 0.962389 0.0521163
\(342\) 0 0
\(343\) 17.1900i 0.928171i
\(344\) 0 0
\(345\) −5.92478 6.70052i −0.318979 0.360744i
\(346\) 0 0
\(347\) 20.1925i 1.08399i −0.840381 0.541996i \(-0.817669\pi\)
0.840381 0.541996i \(-0.182331\pi\)
\(348\) 0 0
\(349\) 27.2506 1.45869 0.729346 0.684145i \(-0.239825\pi\)
0.729346 + 0.684145i \(0.239825\pi\)
\(350\) 0 0
\(351\) −5.11871 −0.273217
\(352\) 0 0
\(353\) 5.02302i 0.267349i −0.991025 0.133674i \(-0.957322\pi\)
0.991025 0.133674i \(-0.0426776\pi\)
\(354\) 0 0
\(355\) −10.8872 12.3127i −0.577831 0.653488i
\(356\) 0 0
\(357\) 12.7513i 0.674871i
\(358\) 0 0
\(359\) −18.1768 −0.959334 −0.479667 0.877450i \(-0.659243\pi\)
−0.479667 + 0.877450i \(0.659243\pi\)
\(360\) 0 0
\(361\) 1.92619 0.101379
\(362\) 0 0
\(363\) 1.00000i 0.0524864i
\(364\) 0 0
\(365\) −10.7513 + 9.50659i −0.562749 + 0.497598i
\(366\) 0 0
\(367\) 8.56467i 0.447072i 0.974696 + 0.223536i \(0.0717600\pi\)
−0.974696 + 0.223536i \(0.928240\pi\)
\(368\) 0 0
\(369\) 2.38787 0.124308
\(370\) 0 0
\(371\) 18.4485 0.957799
\(372\) 0 0
\(373\) 7.81924i 0.404865i −0.979296 0.202432i \(-0.935115\pi\)
0.979296 0.202432i \(-0.0648846\pi\)
\(374\) 0 0
\(375\) −6.32487 9.21933i −0.326615 0.476084i
\(376\) 0 0
\(377\) 12.2228i 0.629508i
\(378\) 0 0
\(379\) 1.14903 0.0590218 0.0295109 0.999564i \(-0.490605\pi\)
0.0295109 + 0.999564i \(0.490605\pi\)
\(380\) 0 0
\(381\) −12.4182 −0.636203
\(382\) 0 0
\(383\) 34.0870i 1.74176i 0.491493 + 0.870882i \(0.336451\pi\)
−0.491493 + 0.870882i \(0.663549\pi\)
\(384\) 0 0
\(385\) −4.70052 + 4.15633i −0.239561 + 0.211826i
\(386\) 0 0
\(387\) 2.80606i 0.142640i
\(388\) 0 0
\(389\) −23.7743 −1.20541 −0.602703 0.797965i \(-0.705910\pi\)
−0.602703 + 0.797965i \(0.705910\pi\)
\(390\) 0 0
\(391\) −18.1768 −0.919240
\(392\) 0 0
\(393\) 5.92478i 0.298865i
\(394\) 0 0
\(395\) −2.00000 2.26187i −0.100631 0.113807i
\(396\) 0 0
\(397\) 4.15045i 0.208305i −0.994561 0.104152i \(-0.966787\pi\)
0.994561 0.104152i \(-0.0332130\pi\)
\(398\) 0 0
\(399\) 12.8364 0.642623
\(400\) 0 0
\(401\) −33.9149 −1.69363 −0.846815 0.531887i \(-0.821483\pi\)
−0.846815 + 0.531887i \(0.821483\pi\)
\(402\) 0 0
\(403\) 4.92619i 0.245391i
\(404\) 0 0
\(405\) −1.48119 1.67513i −0.0736011 0.0832379i
\(406\) 0 0
\(407\) 1.61213i 0.0799102i
\(408\) 0 0
\(409\) −8.55008 −0.422774 −0.211387 0.977402i \(-0.567798\pi\)
−0.211387 + 0.977402i \(0.567798\pi\)
\(410\) 0 0
\(411\) 9.79877 0.483338
\(412\) 0 0
\(413\) 37.2506i 1.83298i
\(414\) 0 0
\(415\) −1.35026 + 1.19394i −0.0662817 + 0.0586080i
\(416\) 0 0
\(417\) 2.12601i 0.104111i
\(418\) 0 0
\(419\) 13.2995 0.649722 0.324861 0.945762i \(-0.394682\pi\)
0.324861 + 0.945762i \(0.394682\pi\)
\(420\) 0 0
\(421\) 33.3014 1.62301 0.811505 0.584345i \(-0.198649\pi\)
0.811505 + 0.584345i \(0.198649\pi\)
\(422\) 0 0
\(423\) 4.31265i 0.209688i
\(424\) 0 0
\(425\) −22.5501 2.78163i −1.09384 0.134929i
\(426\) 0 0
\(427\) 22.2374i 1.07614i
\(428\) 0 0
\(429\) 5.11871 0.247134
\(430\) 0 0
\(431\) −2.07522 −0.0999600 −0.0499800 0.998750i \(-0.515916\pi\)
−0.0499800 + 0.998750i \(0.515916\pi\)
\(432\) 0 0
\(433\) 37.4010i 1.79738i 0.438585 + 0.898690i \(0.355480\pi\)
−0.438585 + 0.898690i \(0.644520\pi\)
\(434\) 0 0
\(435\) −4.00000 + 3.53690i −0.191785 + 0.169582i
\(436\) 0 0
\(437\) 18.2981i 0.875315i
\(438\) 0 0
\(439\) −6.02444 −0.287531 −0.143765 0.989612i \(-0.545921\pi\)
−0.143765 + 0.989612i \(0.545921\pi\)
\(440\) 0 0
\(441\) 0.873992 0.0416187
\(442\) 0 0
\(443\) 10.1359i 0.481569i −0.970579 0.240785i \(-0.922595\pi\)
0.970579 0.240785i \(-0.0774047\pi\)
\(444\) 0 0
\(445\) −4.38787 4.96239i −0.208005 0.235240i
\(446\) 0 0
\(447\) 8.31265i 0.393175i
\(448\) 0 0
\(449\) 11.4861 0.542063 0.271032 0.962570i \(-0.412635\pi\)
0.271032 + 0.962570i \(0.412635\pi\)
\(450\) 0 0
\(451\) −2.38787 −0.112441
\(452\) 0 0
\(453\) 15.2750i 0.717684i
\(454\) 0 0
\(455\) −21.2750 24.0606i −0.997389 1.12798i
\(456\) 0 0
\(457\) 15.0435i 0.703705i −0.936055 0.351852i \(-0.885552\pi\)
0.936055 0.351852i \(-0.114448\pi\)
\(458\) 0 0
\(459\) −4.54420 −0.212105
\(460\) 0 0
\(461\) −26.2374 −1.22200 −0.610999 0.791631i \(-0.709232\pi\)
−0.610999 + 0.791631i \(0.709232\pi\)
\(462\) 0 0
\(463\) 5.46168i 0.253826i −0.991914 0.126913i \(-0.959493\pi\)
0.991914 0.126913i \(-0.0405069\pi\)
\(464\) 0 0
\(465\) −1.61213 + 1.42548i −0.0747606 + 0.0661053i
\(466\) 0 0
\(467\) 2.70052i 0.124965i 0.998046 + 0.0624827i \(0.0199018\pi\)
−0.998046 + 0.0624827i \(0.980098\pi\)
\(468\) 0 0
\(469\) −30.0263 −1.38649
\(470\) 0 0
\(471\) 7.01317 0.323150
\(472\) 0 0
\(473\) 2.80606i 0.129023i
\(474\) 0 0
\(475\) 2.80018 22.7005i 0.128481 1.04157i
\(476\) 0 0
\(477\) 6.57452i 0.301026i
\(478\) 0 0
\(479\) 16.7757 0.766503 0.383252 0.923644i \(-0.374804\pi\)
0.383252 + 0.923644i \(0.374804\pi\)
\(480\) 0 0
\(481\) −8.25202 −0.376260
\(482\) 0 0
\(483\) 11.2243i 0.510721i
\(484\) 0 0
\(485\) −16.6253 + 14.7005i −0.754916 + 0.667516i
\(486\) 0 0
\(487\) 34.3996i 1.55880i 0.626529 + 0.779398i \(0.284475\pi\)
−0.626529 + 0.779398i \(0.715525\pi\)
\(488\) 0 0
\(489\) 6.76116 0.305750
\(490\) 0 0
\(491\) −14.9525 −0.674799 −0.337399 0.941362i \(-0.609547\pi\)
−0.337399 + 0.941362i \(0.609547\pi\)
\(492\) 0 0
\(493\) 10.8510i 0.488703i
\(494\) 0 0
\(495\) 1.48119 + 1.67513i 0.0665747 + 0.0752915i
\(496\) 0 0
\(497\) 20.6253i 0.925171i
\(498\) 0 0
\(499\) −2.85097 −0.127627 −0.0638135 0.997962i \(-0.520326\pi\)
−0.0638135 + 0.997962i \(0.520326\pi\)
\(500\) 0 0
\(501\) 11.8192 0.528045
\(502\) 0 0
\(503\) 1.48024i 0.0660006i 0.999455 + 0.0330003i \(0.0105062\pi\)
−0.999455 + 0.0330003i \(0.989494\pi\)
\(504\) 0 0
\(505\) 20.1622 + 22.8021i 0.897206 + 1.01468i
\(506\) 0 0
\(507\) 13.2012i 0.586287i
\(508\) 0 0
\(509\) 23.2995 1.03273 0.516366 0.856368i \(-0.327285\pi\)
0.516366 + 0.856368i \(0.327285\pi\)
\(510\) 0 0
\(511\) −18.0098 −0.796709
\(512\) 0 0
\(513\) 4.57452i 0.201970i
\(514\) 0 0
\(515\) 27.3258 24.1622i 1.20412 1.06471i
\(516\) 0 0
\(517\) 4.31265i 0.189670i
\(518\) 0 0
\(519\) −6.99271 −0.306946
\(520\) 0 0
\(521\) −6.81194 −0.298437 −0.149218 0.988804i \(-0.547676\pi\)
−0.149218 + 0.988804i \(0.547676\pi\)
\(522\) 0 0
\(523\) 16.0567i 0.702109i −0.936355 0.351054i \(-0.885823\pi\)
0.936355 0.351054i \(-0.114177\pi\)
\(524\) 0 0
\(525\) 1.71767 13.9248i 0.0749651 0.607727i
\(526\) 0 0
\(527\) 4.37328i 0.190503i
\(528\) 0 0
\(529\) 7.00000 0.304348
\(530\) 0 0
\(531\) 13.2750 0.576088
\(532\) 0 0
\(533\) 12.2228i 0.529430i
\(534\) 0 0
\(535\) 15.7988 13.9697i 0.683040 0.603962i
\(536\) 0 0
\(537\) 2.70052i 0.116536i
\(538\) 0 0
\(539\) −0.873992 −0.0376455
\(540\) 0 0
\(541\) 6.62530 0.284844 0.142422 0.989806i \(-0.454511\pi\)
0.142422 + 0.989806i \(0.454511\pi\)
\(542\) 0 0
\(543\) 21.1998i 0.909771i
\(544\) 0 0
\(545\) −22.8119 25.7988i −0.977156 1.10510i
\(546\) 0 0
\(547\) 5.75860i 0.246220i 0.992393 + 0.123110i \(0.0392868\pi\)
−0.992393 + 0.123110i \(0.960713\pi\)
\(548\) 0 0
\(549\) −7.92478 −0.338221
\(550\) 0 0
\(551\) −10.9234 −0.465351
\(552\) 0 0
\(553\) 3.78892i 0.161121i
\(554\) 0 0
\(555\) −2.38787 2.70052i −0.101360 0.114631i
\(556\) 0 0
\(557\) 19.8700i 0.841920i 0.907079 + 0.420960i \(0.138307\pi\)
−0.907079 + 0.420960i \(0.861693\pi\)
\(558\) 0 0
\(559\) −14.3634 −0.607509
\(560\) 0 0
\(561\) 4.54420 0.191856
\(562\) 0 0
\(563\) 5.83383i 0.245866i 0.992415 + 0.122933i \(0.0392301\pi\)
−0.992415 + 0.122933i \(0.960770\pi\)
\(564\) 0 0
\(565\) 23.0132 20.3488i 0.968171 0.856082i
\(566\) 0 0
\(567\) 2.80606i 0.117844i
\(568\) 0 0
\(569\) −46.7123 −1.95828 −0.979140 0.203185i \(-0.934871\pi\)
−0.979140 + 0.203185i \(0.934871\pi\)
\(570\) 0 0
\(571\) 24.4241 1.02212 0.511058 0.859546i \(-0.329254\pi\)
0.511058 + 0.859546i \(0.329254\pi\)
\(572\) 0 0
\(573\) 13.1490i 0.549309i
\(574\) 0 0
\(575\) −19.8496 2.44851i −0.827784 0.102110i
\(576\) 0 0
\(577\) 16.5647i 0.689596i 0.938677 + 0.344798i \(0.112053\pi\)
−0.938677 + 0.344798i \(0.887947\pi\)
\(578\) 0 0
\(579\) −5.89446 −0.244965
\(580\) 0 0
\(581\) −2.26187 −0.0938380
\(582\) 0 0
\(583\) 6.57452i 0.272289i
\(584\) 0 0
\(585\) −8.57452 + 7.58181i −0.354513 + 0.313469i
\(586\) 0 0
\(587\) 27.3258i 1.12786i −0.825823 0.563929i \(-0.809289\pi\)
0.825823 0.563929i \(-0.190711\pi\)
\(588\) 0 0
\(589\) −4.40246 −0.181400
\(590\) 0 0
\(591\) 20.3938 0.838887
\(592\) 0 0
\(593\) 12.6048i 0.517618i 0.965928 + 0.258809i \(0.0833301\pi\)
−0.965928 + 0.258809i \(0.916670\pi\)
\(594\) 0 0
\(595\) −18.8872 21.3601i −0.774298 0.875679i
\(596\) 0 0
\(597\) 17.4010i 0.712177i
\(598\) 0 0
\(599\) 10.5990 0.433061 0.216531 0.976276i \(-0.430526\pi\)
0.216531 + 0.976276i \(0.430526\pi\)
\(600\) 0 0
\(601\) −22.4749 −0.916768 −0.458384 0.888754i \(-0.651572\pi\)
−0.458384 + 0.888754i \(0.651572\pi\)
\(602\) 0 0
\(603\) 10.7005i 0.435759i
\(604\) 0 0
\(605\) −1.48119 1.67513i −0.0602191 0.0681038i
\(606\) 0 0
\(607\) 33.5183i 1.36047i −0.732995 0.680234i \(-0.761878\pi\)
0.732995 0.680234i \(-0.238122\pi\)
\(608\) 0 0
\(609\) −6.70052 −0.271519
\(610\) 0 0
\(611\) −22.0752 −0.893068
\(612\) 0 0
\(613\) 11.5672i 0.467196i −0.972333 0.233598i \(-0.924950\pi\)
0.972333 0.233598i \(-0.0750499\pi\)
\(614\) 0 0
\(615\) 4.00000 3.53690i 0.161296 0.142622i
\(616\) 0 0
\(617\) 33.3357i 1.34204i −0.741438 0.671022i \(-0.765856\pi\)
0.741438 0.671022i \(-0.234144\pi\)
\(618\) 0 0
\(619\) 4.43866 0.178405 0.0892024 0.996014i \(-0.471568\pi\)
0.0892024 + 0.996014i \(0.471568\pi\)
\(620\) 0 0
\(621\) −4.00000 −0.160514
\(622\) 0 0
\(623\) 8.31265i 0.333039i
\(624\) 0 0
\(625\) −24.2506 6.07522i −0.970024 0.243009i
\(626\) 0 0
\(627\) 4.57452i 0.182689i
\(628\) 0 0
\(629\) −7.32582 −0.292100
\(630\) 0 0
\(631\) 39.8496 1.58639 0.793193 0.608971i \(-0.208417\pi\)
0.793193 + 0.608971i \(0.208417\pi\)
\(632\) 0 0
\(633\) 18.1260i 0.720444i
\(634\) 0 0
\(635\) −20.8021 + 18.3938i −0.825506 + 0.729934i
\(636\) 0 0
\(637\) 4.47371i 0.177255i
\(638\) 0 0
\(639\) −7.35026 −0.290772
\(640\) 0 0
\(641\) −3.88858 −0.153590 −0.0767948 0.997047i \(-0.524469\pi\)
−0.0767948 + 0.997047i \(0.524469\pi\)
\(642\) 0 0
\(643\) 40.9380i 1.61444i 0.590254 + 0.807218i \(0.299028\pi\)
−0.590254 + 0.807218i \(0.700972\pi\)
\(644\) 0 0
\(645\) −4.15633 4.70052i −0.163655 0.185083i
\(646\) 0 0
\(647\) 1.76257i 0.0692939i −0.999400 0.0346469i \(-0.988969\pi\)
0.999400 0.0346469i \(-0.0110307\pi\)
\(648\) 0 0
\(649\) −13.2750 −0.521091
\(650\) 0 0
\(651\) −2.70052 −0.105842
\(652\) 0 0
\(653\) 7.03761i 0.275403i 0.990474 + 0.137702i \(0.0439715\pi\)
−0.990474 + 0.137702i \(0.956029\pi\)
\(654\) 0 0
\(655\) 8.77575 + 9.92478i 0.342897 + 0.387793i
\(656\) 0 0
\(657\) 6.41819i 0.250397i
\(658\) 0 0
\(659\) −12.6253 −0.491812 −0.245906 0.969294i \(-0.579085\pi\)
−0.245906 + 0.969294i \(0.579085\pi\)
\(660\) 0 0
\(661\) 13.2243 0.514364 0.257182 0.966363i \(-0.417206\pi\)
0.257182 + 0.966363i \(0.417206\pi\)
\(662\) 0 0
\(663\) 23.2605i 0.903361i
\(664\) 0 0
\(665\) 21.5026 19.0132i 0.833836 0.737299i
\(666\) 0 0
\(667\) 9.55149i 0.369835i
\(668\) 0 0
\(669\) 23.6385 0.913916
\(670\) 0 0
\(671\) 7.92478 0.305933
\(672\) 0 0
\(673\) 18.2677i 0.704170i −0.935968 0.352085i \(-0.885473\pi\)
0.935968 0.352085i \(-0.114527\pi\)
\(674\) 0 0
\(675\) −4.96239 0.612127i −0.191002 0.0235608i
\(676\) 0 0
\(677\) 33.0191i 1.26903i −0.772912 0.634513i \(-0.781201\pi\)
0.772912 0.634513i \(-0.218799\pi\)
\(678\) 0 0
\(679\) −27.8496 −1.06877
\(680\) 0 0
\(681\) 1.26916 0.0486343
\(682\) 0 0
\(683\) 30.8627i 1.18093i 0.807063 + 0.590465i \(0.201056\pi\)
−0.807063 + 0.590465i \(0.798944\pi\)
\(684\) 0 0
\(685\) 16.4142 14.5139i 0.627155 0.554547i
\(686\) 0 0
\(687\) 16.1768i 0.617183i
\(688\) 0 0
\(689\) −33.6531 −1.28208
\(690\) 0 0
\(691\) −27.6991 −1.05372 −0.526862 0.849951i \(-0.676631\pi\)
−0.526862 + 0.849951i \(0.676631\pi\)
\(692\) 0 0
\(693\) 2.80606i 0.106594i
\(694\) 0 0
\(695\) 3.14903 + 3.56134i 0.119450 + 0.135089i
\(696\) 0 0
\(697\) 10.8510i 0.411010i
\(698\) 0 0
\(699\) 18.4690 0.698561
\(700\) 0 0
\(701\) −38.9643 −1.47166 −0.735831 0.677166i \(-0.763208\pi\)
−0.735831 + 0.677166i \(0.763208\pi\)
\(702\) 0 0
\(703\) 7.37470i 0.278142i
\(704\) 0 0
\(705\) −6.38787 7.22425i −0.240581 0.272081i
\(706\) 0 0
\(707\) 38.1965i 1.43653i
\(708\) 0 0
\(709\) 4.32250 0.162335 0.0811674 0.996700i \(-0.474135\pi\)
0.0811674 + 0.996700i \(0.474135\pi\)
\(710\) 0 0
\(711\) −1.35026 −0.0506388
\(712\) 0 0
\(713\) 3.84955i 0.144167i
\(714\) 0 0
\(715\) 8.57452 7.58181i 0.320669 0.283544i
\(716\) 0 0
\(717\) 19.3258i 0.721736i
\(718\) 0 0
\(719\) −38.3996 −1.43206 −0.716032 0.698067i \(-0.754044\pi\)
−0.716032 + 0.698067i \(0.754044\pi\)
\(720\) 0 0
\(721\) 45.7743 1.70473
\(722\) 0 0
\(723\) 28.5501i 1.06179i
\(724\) 0 0
\(725\) −1.46168 + 11.8496i −0.0542855 + 0.440081i
\(726\) 0 0
\(727\) 21.6728i 0.803798i 0.915684 + 0.401899i \(0.131650\pi\)
−0.915684 + 0.401899i \(0.868350\pi\)
\(728\) 0 0
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) −12.7513 −0.471624
\(732\) 0 0
\(733\) 25.0698i 0.925976i −0.886365 0.462988i \(-0.846777\pi\)
0.886365 0.462988i \(-0.153223\pi\)
\(734\) 0 0
\(735\) 1.46405 1.29455i 0.0540023 0.0477503i
\(736\) 0 0
\(737\) 10.7005i 0.394159i
\(738\) 0 0
\(739\) −18.9018 −0.695312 −0.347656 0.937622i \(-0.613022\pi\)
−0.347656 + 0.937622i \(0.613022\pi\)
\(740\) 0 0
\(741\) −23.4156 −0.860195
\(742\) 0 0
\(743\) 43.6688i 1.60205i 0.598629 + 0.801026i \(0.295712\pi\)
−0.598629 + 0.801026i \(0.704288\pi\)
\(744\) 0 0
\(745\) 12.3127 + 13.9248i 0.451101 + 0.510164i
\(746\) 0 0
\(747\) 0.806063i 0.0294923i
\(748\) 0 0
\(749\) 26.4650 0.967010
\(750\) 0 0
\(751\) 47.0541 1.71703 0.858514 0.512789i \(-0.171388\pi\)
0.858514 + 0.512789i \(0.171388\pi\)
\(752\) 0 0
\(753\) 23.1998i 0.845448i
\(754\) 0 0
\(755\) −22.6253 25.5877i −0.823419 0.931231i
\(756\) 0 0
\(757\) 26.9116i 0.978119i −0.872250 0.489059i \(-0.837340\pi\)
0.872250 0.489059i \(-0.162660\pi\)
\(758\) 0 0
\(759\) 4.00000 0.145191
\(760\) 0 0
\(761\) 16.6859 0.604865 0.302432 0.953171i \(-0.402201\pi\)
0.302432 + 0.953171i \(0.402201\pi\)
\(762\) 0 0
\(763\) 43.2163i 1.56454i
\(764\) 0 0
\(765\) −7.61213 + 6.73084i −0.275217 + 0.243354i
\(766\) 0 0
\(767\) 67.9511i 2.45357i
\(768\) 0 0
\(769\) −23.2995 −0.840201 −0.420100 0.907478i \(-0.638005\pi\)
−0.420100 + 0.907478i \(0.638005\pi\)
\(770\) 0 0
\(771\) −10.8872 −0.392092
\(772\) 0 0
\(773\) 1.63656i 0.0588631i 0.999567 + 0.0294316i \(0.00936971\pi\)
−0.999567 + 0.0294316i \(0.990630\pi\)
\(774\) 0 0
\(775\) −0.589104 + 4.77575i −0.0211612 + 0.171550i
\(776\) 0 0
\(777\) 4.52373i 0.162288i
\(778\) 0 0
\(779\) 10.9234 0.391370
\(780\) 0 0
\(781\) 7.35026 0.263013
\(782\) 0 0
\(783\) 2.38787i 0.0853356i
\(784\) 0 0
\(785\) 11.7480 10.3879i 0.419304 0.370759i
\(786\) 0 0
\(787\) 2.09095i 0.0745344i 0.999305 + 0.0372672i \(0.0118653\pi\)
−0.999305 + 0.0372672i \(0.988135\pi\)
\(788\) 0 0
\(789\) 9.11871 0.324635
\(790\) 0 0
\(791\) 38.5501 1.37068
\(792\) 0 0
\(793\) 40.5647i 1.44049i
\(794\) 0 0
\(795\) −9.73813 11.0132i −0.345376 0.390597i
\(796\) 0 0